"if x and y are doubles and x > y, then we have shown that double_as_int64(x) > double_as_int64(y)"
This only applies for numbers of the same sign though. As soon as the sign changes, the relation breaks since floating point numbers use an independent sign bit while int64 is 2's complement.
double_as_int64 as defined in the linked source code does take care of the sign so that double_as_int64(x) == -double_as_int64(-x). This is also important for the negative zero case.
This only applies for numbers of the same sign though. As soon as the sign changes, the relation breaks since floating point numbers use an independent sign bit while int64 is 2's complement.